We are looking at adding a toilet and sink in a small closet. The area is on a crawl space and there is an unused closet behind it where I can connect the sink vent and install a 5' tall 3" stack with a 3" air admittance valve. We are also looking at adding a washer upstairs. We thought we might use a 2" air admittance valve there too. Will this setup work well? See photo. Any suggestions would be greatly appreciated. How how would the air admittance valves need to be in relation to sink or washer drain?